Numerical analysis of modified gingerbreadman map and itssynchronization in a multiplex network

Gingerbreadman maps are two-dimensional mathematical model in dynamical systems that depicts chaotic behavior and has the ability to generate complex patterns when iterated. The numerical analysis of a modified Gingerbreadman map and its synchronization in a multiplex network is presented in this paper. A thorough numerical analysis of this model reveals a rich transition between periodic, quasi-periodic, and chaotic regimes. The domain of synchronization is probed by designing a three-layer network of 200 chaotic modified Gingerbreadman maps. The numerical analysis of this domain through interlayer coupling force reveals the layers to be desynchronous or synchronous state. The inherent unpredictability of this model renders it a promising candidate for cryptographic applications, particularly in the generation of robust pseudo-random numbers. These numbers exhibit exceptional resistance to attack, thereby enhancing the security of scientific data, as well as facilitating secure communication, leading to economic development.